A mass is attached to the end of a spring and set into oscillation on a horizont

Question

A mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a stretched position of x = +0.150 m. The mass of the block is m = 0.587 kg, the force constant of the spring is k = 61.3 N/m. Determine the following.

(a) force component that the spring exerts on the block just before the block is released (Indicate the direction with the sign of your answer.) N

(b) angular frequency of the resulting oscillatory motion rad/s

(c) maximum speed of the oscillating mass m/s

(d) magnitude of the maximum acceleration of the oscillating mass m/s2

Explanation / Answer

k =61.3 N/m , x =0.15 m , m=0.587 kg

(a) From Hooks law F = -kx

F = -61.3*0.15 = -9.195 N

(v) w = (k/m)^1/2 = (61.3/0.587)^0.5 = 10.22 rad/s

(c) v = Aw = 0.15*10.22 = 1.533 m/s

(d) a = Aw^2 = 0.15*10.22*10.22 = 15.67 m/s^2

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